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Die Näherungslösung ist ein Streckenzug, daher der Name ",[568,1167,553],{},".",[564,1170,1171,1172,1168],{},"Das Verfahren entspricht dem Abbruch der Taylorreihe nach dem linearen Glied: ",[577,1173,1175,1230],{"className":1174},[580],[577,1176,1178],{"className":1177},[584],[586,1179,1180],{"xmlns":588},[590,1181,1182,1227],{},[593,1183,1184,1186,1188,1190,1192,1194,1196,1199,1201,1203,1205,1207,1209,1211,1215,1221,1223,1225],{},[599,1185,601],{},[603,1187,617],{"stretchy":616},[599,1189,620],{},[603,1191,1097],{},[599,1193,915],{},[603,1195,629],{"stretchy":616},[603,1197,1198],{},"≈",[599,1200,601],{},[603,1202,617],{"stretchy":616},[599,1204,620],{},[603,1206,629],{"stretchy":616},[603,1208,1097],{},[599,1210,915],{},[1212,1213,1214],"mtext",{}," ",[596,1216,1217,1219],{},[599,1218,601],{},[603,1220,607],{"mathvariant":605,"lspace":606,"rspace":606},[603,1222,617],{"stretchy":616},[599,1224,620],{},[603,1226,629],{"stretchy":616},[631,1228,1229],{"encoding":633},"y(t + h) \\approx y(t) + h \\, y'(t)",[577,1231,1233,1258,1279,1306],{"className":1232,"ariaHidden":623},[638],[577,1234,1236,1239,1242,1245,1248,1252,1255],{"className":1235},[642],[577,1237],{"className":1238,"style":713},[646],[577,1240,601],{"className":1241,"style":656},[651,655],[577,1243,617],{"className":1244},[721],[577,1246,620],{"className":1247},[651,655],[577,1249],{"className":1250,"style":1251},[698],"margin-right:0.2222em;",[577,1253,1097],{"className":1254},[1149],[577,1256],{"className":1257,"style":1251},[698],[577,1259,1261,1264,1267,1270,1273,1276],{"className":1260},[642],[577,1262],{"className":1263,"style":713},[646],[577,1265,915],{"className":1266},[651,655],[577,1268,629],{"className":1269},[739],[577,1271],{"className":1272,"style":699},[698],[577,1274,1198],{"className":1275},[703],[577,1277],{"className":1278,"style":699},[698],[577,1280,1282,1285,1288,1291,1294,1297,1300,1303],{"className":1281},[642],[577,1283],{"className":1284,"style":713},[646],[577,1286,601],{"className":1287,"style":656},[651,655],[577,1289,617],{"className":1290},[721],[577,1292,620],{"className":1293},[651,655],[577,1295,629],{"className":1296},[739],[577,1298],{"className":1299,"style":1251},[698],[577,1301,1097],{"className":1302},[1149],[577,1304],{"className":1305,"style":1251},[698],[577,1307,1309,1313,1316,1319,1351,1354,1357],{"className":1308},[642],[577,1310],{"className":1311,"style":1312},[646],"height:1.0019em;vertical-align:-0.25em;",[577,1314,915],{"className":1315},[651,655],[577,1317],{"className":1318,"style":732},[698],[577,1320,1322,1325],{"className":1321},[651],[577,1323,601],{"className":1324,"style":656},[651,655],[577,1326,1328],{"className":1327},[660],[577,1329,1331],{"className":1330},[664],[577,1332,1334],{"className":1333},[668],[577,1335,1337],{"className":1336,"style":673},[672],[577,1338,1339,1342],{"style":676},[577,1340],{"className":1341,"style":681},[680],[577,1343,1345],{"className":1344},[685,686,687,688],[577,1346,1348],{"className":1347},[651,688],[577,1349,607],{"className":1350},[651,688],[577,1352,617],{"className":1353},[721],[577,1355,620],{"className":1356},[651,655],[577,1358,629],{"className":1359},[739],[564,1361,1362],{},"Eigenschaften:",[1364,1365,1366,1431,1524],"ul",{},[1367,1368,1369,1372,1373,1401,1402,1430],"li",{},[568,1370,1371],{},"Konvergenzordnung 1",": Der globale Fehler an einem festen Zeitpunkt ist proportional zu ",[577,1374,1376,1389],{"className":1375},[580],[577,1377,1379],{"className":1378},[584],[586,1380,1381],{"xmlns":588},[590,1382,1383,1387],{},[593,1384,1385],{},[599,1386,915],{},[631,1388,915],{"encoding":633},[577,1390,1392],{"className":1391,"ariaHidden":623},[638],[577,1393,1395,1398],{"className":1394},[642],[577,1396],{"className":1397,"style":927},[646],[577,1399,915],{"className":1400},[651,655],". Halbiert man ",[577,1403,1405,1418],{"className":1404},[580],[577,1406,1408],{"className":1407},[584],[586,1409,1410],{"xmlns":588},[590,1411,1412,1416],{},[593,1413,1414],{},[599,1415,915],{},[631,1417,915],{"encoding":633},[577,1419,1421],{"className":1420,"ariaHidden":623},[638],[577,1422,1424,1427],{"className":1423},[642],[577,1425],{"className":1426,"style":927},[646],[577,1428,915],{"className":1429},[651,655],", halbiert sich der Fehler ungefähr.",[1367,1432,1433,1436,1437,1523],{},[568,1434,1435],{},"Explizit",": ",[577,1438,1440,1464],{"className":1439},[580],[577,1441,1443],{"className":1442},[584],[586,1444,1445],{"xmlns":588},[590,1446,1447,1461],{},[593,1448,1449],{},[758,1450,1451,1453],{},[599,1452,601],{},[593,1454,1455,1457,1459],{},[599,1456,954],{},[603,1458,1097],{},[763,1460,1100],{},[631,1462,1463],{"encoding":633},"y_{k+1}",[577,1465,1467],{"className":1466,"ariaHidden":623},[638],[577,1468,1470,1474],{"className":1469},[642],[577,1471],{"className":1472,"style":1473},[646],"height:0.6389em;vertical-align:-0.2083em;",[577,1475,1477,1480],{"className":1476},[651],[577,1478,601],{"className":1479,"style":656},[651,655],[577,1481,1483],{"className":1482},[660],[577,1484,1486,1515],{"className":1485},[664,806],[577,1487,1489,1512],{"className":1488},[668],[577,1490,1492],{"className":1491,"style":1001},[672],[577,1493,1494,1497],{"style":879},[577,1495],{"className":1496,"style":681},[680],[577,1498,1500],{"className":1499},[685,686,687,688],[577,1501,1503,1506,1509],{"className":1502},[651,688],[577,1504,954],{"className":1505,"style":1013},[651,655,688],[577,1507,1097],{"className":1508},[1149,688],[577,1510,1100],{"className":1511},[651,688],[577,1513,830],{"className":1514},[829],[577,1516,1518],{"className":1517},[668],[577,1519,1521],{"className":1520,"style":1162},[672],[577,1522],{}," ergibt sich direkt aus bekannten Werten, ohne Gleichung zu lösen.",[1367,1525,1526,1529,1530,1558,1559,1650,1651,1705,1706,1791,1792,1936],{},[568,1527,1528],{},"Stabilität",": Bei abklingenden Lösungen muss ",[577,1531,1533,1546],{"className":1532},[580],[577,1534,1536],{"className":1535},[584],[586,1537,1538],{"xmlns":588},[590,1539,1540,1544],{},[593,1541,1542],{},[599,1543,915],{},[631,1545,915],{"encoding":633},[577,1547,1549],{"className":1548,"ariaHidden":623},[638],[577,1550,1552,1555],{"className":1551},[642],[577,1553],{"className":1554,"style":927},[646],[577,1556,915],{"className":1557},[651,655]," klein genug sein. Für ",[577,1560,1562,1587],{"className":1561},[580],[577,1563,1565],{"className":1564},[584],[586,1566,1567],{"xmlns":588},[590,1568,1569,1584],{},[593,1570,1571,1577,1579,1582],{},[596,1572,1573,1575],{},[599,1574,601],{},[603,1576,607],{"mathvariant":605,"lspace":606,"rspace":606},[603,1578,610],{},[599,1580,1581],{},"λ",[599,1583,601],{},[631,1585,1586],{"encoding":633},"y' = \\lambda y",[577,1588,1590,1637],{"className":1589,"ariaHidden":623},[638],[577,1591,1593,1596,1628,1631,1634],{"className":1592},[642],[577,1594],{"className":1595,"style":647},[646],[577,1597,1599,1602],{"className":1598},[651],[577,1600,601],{"className":1601,"style":656},[651,655],[577,1603,1605],{"className":1604},[660],[577,1606,1608],{"className":1607},[664],[577,1609,1611],{"className":1610},[668],[577,1612,1614],{"className":1613,"style":673},[672],[577,1615,1616,1619],{"style":676},[577,1617],{"className":1618,"style":681},[680],[577,1620,1622],{"className":1621},[685,686,687,688],[577,1623,1625],{"className":1624},[651,688],[577,1626,607],{"className":1627},[651,688],[577,1629],{"className":1630,"style":699},[698],[577,1632,610],{"className":1633},[703],[577,1635],{"className":1636,"style":699},[698],[577,1638,1640,1644,1647],{"className":1639},[642],[577,1641],{"className":1642,"style":1643},[646],"height:0.8889em;vertical-align:-0.1944em;",[577,1645,1581],{"className":1646},[651,655],[577,1648,601],{"className":1649,"style":656},[651,655]," mit ",[577,1652,1654,1673],{"className":1653},[580],[577,1655,1657],{"className":1656},[584],[586,1658,1659],{"xmlns":588},[590,1660,1661,1670],{},[593,1662,1663,1665,1668],{},[599,1664,1581],{},[603,1666,1667],{},"\u003C",[763,1669,765],{},[631,1671,1672],{"encoding":633},"\\lambda \u003C 0",[577,1674,1676,1695],{"className":1675,"ariaHidden":623},[638],[577,1677,1679,1683,1686,1689,1692],{"className":1678},[642],[577,1680],{"className":1681,"style":1682},[646],"height:0.7335em;vertical-align:-0.0391em;",[577,1684,1581],{"className":1685},[651,655],[577,1687],{"className":1688,"style":699},[698],[577,1690,1667],{"className":1691},[703],[577,1693],{"className":1694,"style":699},[698],[577,1696,1698,1702],{"className":1697},[642],[577,1699],{"className":1700,"style":1701},[646],"height:0.6444em;",[577,1703,765],{"className":1704},[651]," ist ",[577,1707,1709,1738],{"className":1708},[580],[577,1710,1712],{"className":1711},[584],[586,1713,1714],{"xmlns":588},[590,1715,1716,1735],{},[593,1717,1718,1721,1723,1725,1727,1729,1731,1733],{},[599,1719,1720],{"mathvariant":605},"∣",[763,1722,1100],{},[603,1724,1097],{},[599,1726,915],{},[599,1728,1581],{},[599,1730,1720],{"mathvariant":605},[603,1732,1667],{},[763,1734,1100],{},[631,1736,1737],{"encoding":633},"|1 + h\\lambda| \u003C 1",[577,1739,1741,1760,1782],{"className":1740,"ariaHidden":623},[638],[577,1742,1744,1747,1751,1754,1757],{"className":1743},[642],[577,1745],{"className":1746,"style":713},[646],[577,1748,1750],{"className":1749},[651],"∣1",[577,1752],{"className":1753,"style":1251},[698],[577,1755,1097],{"className":1756},[1149],[577,1758],{"className":1759,"style":1251},[698],[577,1761,1763,1766,1770,1773,1776,1779],{"className":1762},[642],[577,1764],{"className":1765,"style":713},[646],[577,1767,1769],{"className":1768},[651,655],"hλ",[577,1771,1720],{"className":1772},[651],[577,1774],{"className":1775,"style":699},[698],[577,1777,1667],{"className":1778},[703],[577,1780],{"className":1781,"style":699},[698],[577,1783,1785,1788],{"className":1784},[642],[577,1786],{"className":1787,"style":1701},[646],[577,1789,1100],{"className":1790},[651]," nötig, also ",[577,1793,1795,1825],{"className":1794},[580],[577,1796,1798],{"className":1797},[584],[586,1799,1800],{"xmlns":588},[590,1801,1802,1822],{},[593,1803,1804,1806,1808],{},[599,1805,915],{},[603,1807,1667],{},[1809,1810,1811,1814],"mfrac",{},[763,1812,1813],{},"2",[593,1815,1816,1818,1820],{},[599,1817,1720],{"mathvariant":605},[599,1819,1581],{},[599,1821,1720],{"mathvariant":605},[631,1823,1824],{"encoding":633},"h \u003C \\frac{2}{|\\lambda|}",[577,1826,1828,1846],{"className":1827,"ariaHidden":623},[638],[577,1829,1831,1834,1837,1840,1843],{"className":1830},[642],[577,1832],{"className":1833,"style":1682},[646],[577,1835,915],{"className":1836},[651,655],[577,1838],{"className":1839,"style":699},[698],[577,1841,1667],{"className":1842},[703],[577,1844],{"className":1845,"style":699},[698],[577,1847,1849,1853],{"className":1848},[642],[577,1850],{"className":1851,"style":1852},[646],"height:1.3651em;vertical-align:-0.52em;",[577,1854,1856,1860,1933],{"className":1855},[651],[577,1857],{"className":1858},[721,1859],"nulldelimiter",[577,1861,1863],{"className":1862},[1809],[577,1864,1866,1924],{"className":1865},[664,806],[577,1867,1869,1921],{"className":1868},[668],[577,1870,1873,1895,1906],{"className":1871,"style":1872},[672],"height:0.8451em;",[577,1874,1876,1880],{"style":1875},"top:-2.655em;",[577,1877],{"className":1878,"style":1879},[680],"height:3em;",[577,1881,1883],{"className":1882},[685,686,687,688],[577,1884,1886,1889,1892],{"className":1885},[651,688],[577,1887,1720],{"className":1888},[651,688],[577,1890,1581],{"className":1891},[651,655,688],[577,1893,1720],{"className":1894},[651,688],[577,1896,1898,1901],{"style":1897},"top:-3.23em;",[577,1899],{"className":1900,"style":1879},[680],[577,1902],{"className":1903,"style":1905},[1904],"frac-line","border-bottom-width:0.04em;",[577,1907,1909,1912],{"style":1908},"top:-3.394em;",[577,1910],{"className":1911,"style":1879},[680],[577,1913,1915],{"className":1914},[685,686,687,688],[577,1916,1918],{"className":1917},[651,688],[577,1919,1813],{"className":1920},[651,688],[577,1922,830],{"className":1923},[829],[577,1925,1927],{"className":1926},[668],[577,1928,1931],{"className":1929,"style":1930},[672],"height:0.52em;",[577,1932],{},[577,1934],{"className":1935},[739,1859],". Sonst schwingt die Näherung mit wachsendem Betrag.",[564,1938,1939,1940,1968,1969,1997],{},"Für ",[577,1941,1943,1956],{"className":1942},[580],[577,1944,1946],{"className":1945},[584],[586,1947,1948],{"xmlns":588},[590,1949,1950,1954],{},[593,1951,1952],{},[599,1953,613],{},[631,1955,613],{"encoding":633},[577,1957,1959],{"className":1958,"ariaHidden":623},[638],[577,1960,1962,1965],{"className":1961},[642],[577,1963],{"className":1964,"style":1643},[646],[577,1966,613],{"className":1967,"style":717},[651,655]," muss eine Lipschitz-Bedingung in ",[577,1970,1972,1985],{"className":1971},[580],[577,1973,1975],{"className":1974},[584],[586,1976,1977],{"xmlns":588},[590,1978,1979,1983],{},[593,1980,1981],{},[599,1982,601],{},[631,1984,601],{"encoding":633},[577,1986,1988],{"className":1987,"ariaHidden":623},[638],[577,1989,1991,1994],{"className":1990},[642],[577,1992],{"className":1993,"style":858},[646],[577,1995,601],{"className":1996,"style":656},[651,655]," gelten, damit die Lösung eindeutig ist und das Verfahren konvergiert.",[559,1999,2001],{"id":2000},"beispiele","Beispiele",[564,2003,2004,740,2088,2154,2155,2238,2239,2291,2292,2355,2356,2408],{},[577,2005,2007,2029],{"className":2006},[580],[577,2008,2010],{"className":2009},[584],[586,2011,2012],{"xmlns":588},[590,2013,2014,2026],{},[593,2015,2016,2022,2024],{},[596,2017,2018,2020],{},[599,2019,601],{},[603,2021,607],{"mathvariant":605,"lspace":606,"rspace":606},[603,2023,610],{},[599,2025,601],{},[631,2027,2028],{"encoding":633},"y' = y",[577,2030,2032,2079],{"className":2031,"ariaHidden":623},[638],[577,2033,2035,2038,2070,2073,2076],{"className":2034},[642],[577,2036],{"className":2037,"style":647},[646],[577,2039,2041,2044],{"className":2040},[651],[577,2042,601],{"className":2043,"style":656},[651,655],[577,2045,2047],{"className":2046},[660],[577,2048,2050],{"className":2049},[664],[577,2051,2053],{"className":2052},[668],[577,2054,2056],{"className":2055,"style":673},[672],[577,2057,2058,2061],{"style":676},[577,2059],{"className":2060,"style":681},[680],[577,2062,2064],{"className":2063},[685,686,687,688],[577,2065,2067],{"className":2066},[651,688],[577,2068,607],{"className":2069},[651,688],[577,2071],{"className":2072,"style":699},[698],[577,2074,610],{"className":2075},[703],[577,2077],{"className":2078,"style":699},[698],[577,2080,2082,2085],{"className":2081},[642],[577,2083],{"className":2084,"style":858},[646],[577,2086,601],{"className":2087,"style":656},[651,655],[577,2089,2091,2115],{"className":2090},[580],[577,2092,2094],{"className":2093},[584],[586,2095,2096],{"xmlns":588},[590,2097,2098,2112],{},[593,2099,2100,2102,2104,2106,2108,2110],{},[599,2101,601],{},[603,2103,617],{"stretchy":616},[763,2105,765],{},[603,2107,629],{"stretchy":616},[603,2109,610],{},[763,2111,1100],{},[631,2113,2114],{"encoding":633},"y(0) = 1",[577,2116,2118,2145],{"className":2117,"ariaHidden":623},[638],[577,2119,2121,2124,2127,2130,2133,2136,2139,2142],{"className":2120},[642],[577,2122],{"className":2123,"style":713},[646],[577,2125,601],{"className":2126,"style":656},[651,655],[577,2128,617],{"className":2129},[721],[577,2131,765],{"className":2132},[651],[577,2134,629],{"className":2135},[739],[577,2137],{"className":2138,"style":699},[698],[577,2140,610],{"className":2141},[703],[577,2143],{"className":2144,"style":699},[698],[577,2146,2148,2151],{"className":2147},[642],[577,2149],{"className":2150,"style":1701},[646],[577,2152,1100],{"className":2153},[651]," mit der exakten Lösung ",[577,2156,2158,2181],{"className":2157},[580],[577,2159,2161],{"className":2160},[584],[586,2162,2163],{"xmlns":588},[590,2164,2165,2178],{},[593,2166,2167,2169,2171],{},[599,2168,601],{},[603,2170,610],{},[596,2172,2173,2176],{},[599,2174,2175],{},"e",[599,2177,620],{},[631,2179,2180],{"encoding":633},"y = e^t",[577,2182,2184,2202],{"className":2183,"ariaHidden":623},[638],[577,2185,2187,2190,2193,2196,2199],{"className":2186},[642],[577,2188],{"className":2189,"style":858},[646],[577,2191,601],{"className":2192,"style":656},[651,655],[577,2194],{"className":2195,"style":699},[698],[577,2197,610],{"className":2198},[703],[577,2200],{"className":2201,"style":699},[698],[577,2203,2205,2209],{"className":2204},[642],[577,2206],{"className":2207,"style":2208},[646],"height:0.7936em;",[577,2210,2212,2215],{"className":2211},[651],[577,2213,2175],{"className":2214},[651,655],[577,2216,2218],{"className":2217},[660],[577,2219,2221],{"className":2220},[664],[577,2222,2224],{"className":2223},[668],[577,2225,2227],{"className":2226,"style":2208},[672],[577,2228,2229,2232],{"style":676},[577,2230],{"className":2231,"style":681},[680],[577,2233,2235],{"className":2234},[685,686,687,688],[577,2236,620],{"className":2237},[651,655,688],". Jeder Schritt multipliziert mit ",[577,2240,2242,2260],{"className":2241},[580],[577,2243,2245],{"className":2244},[584],[586,2246,2247],{"xmlns":588},[590,2248,2249,2257],{},[593,2250,2251,2253,2255],{},[763,2252,1100],{},[603,2254,1097],{},[599,2256,915],{},[631,2258,2259],{"encoding":633},"1 + h",[577,2261,2263,2282],{"className":2262,"ariaHidden":623},[638],[577,2264,2266,2270,2273,2276,2279],{"className":2265},[642],[577,2267],{"className":2268,"style":2269},[646],"height:0.7278em;vertical-align:-0.0833em;",[577,2271,1100],{"className":2272},[651],[577,2274],{"className":2275,"style":1251},[698],[577,2277,1097],{"className":2278},[1149],[577,2280],{"className":2281,"style":1251},[698],[577,2283,2285,2288],{"className":2284},[642],[577,2286],{"className":2287,"style":927},[646],[577,2289,915],{"className":2290},[651,655],". Mit ",[577,2293,2295,2314],{"className":2294},[580],[577,2296,2298],{"className":2297},[584],[586,2299,2300],{"xmlns":588},[590,2301,2302,2311],{},[593,2303,2304,2306,2308],{},[599,2305,915],{},[603,2307,610],{},[763,2309,2310],{},"0,25",[631,2312,2313],{"encoding":633},"h = 0{,}25",[577,2315,2317,2335],{"className":2316,"ariaHidden":623},[638],[577,2318,2320,2323,2326,2329,2332],{"className":2319},[642],[577,2321],{"className":2322,"style":927},[646],[577,2324,915],{"className":2325},[651,655],[577,2327],{"className":2328,"style":699},[698],[577,2330,610],{"className":2331},[703],[577,2333],{"className":2334,"style":699},[698],[577,2336,2338,2342,2345,2351],{"className":2337},[642],[577,2339],{"className":2340,"style":2341},[646],"height:0.8389em;vertical-align:-0.1944em;",[577,2343,765],{"className":2344},[651],[577,2346,2348],{"className":2347},[651],[577,2349,624],{"className":2350},[728],[577,2352,2354],{"className":2353},[651],"25"," erreicht man 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Schritten:",[577,2410,2413],{"className":2411},[2412],"katex-display",[577,2414,2416,2462],{"className":2415},[580],[577,2417,2419],{"className":2418},[584],[586,2420,2422],{"xmlns":588,"display":2421},"block",[590,2423,2424,2459],{},[593,2425,2426,2433,2435,2442,2444,2447,2449,2452,2454,2456],{},[758,2427,2428,2430],{},[599,2429,601],{},[763,2431,2432],{},"4",[603,2434,610],{},[596,2436,2437,2440],{},[763,2438,2439],{},"1,25",[763,2441,2432],{},[603,2443,1198],{},[763,2445,2446],{},"2,4414",[603,2448,624],{"separator":623},[698,2450],{"width":2451},"2em",[599,2453,2175],{},[603,2455,1198],{},[763,2457,2458],{},"2,7183",[631,2460,2461],{"encoding":633},"y_4 = 1{,}25^4 \\approx 2{,}4414, \\qquad e \\approx 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Der Fehler sinkt von ",[577,2881,2883,2898],{"className":2882},[580],[577,2884,2886],{"className":2885},[584],[586,2887,2888],{"xmlns":588},[590,2889,2890,2895],{},[593,2891,2892],{},[763,2893,2894],{},"0,2769",[631,2896,2897],{"encoding":633},"0{,}2769",[577,2899,2901],{"className":2900,"ariaHidden":623},[638],[577,2902,2904,2907,2910,2916],{"className":2903},[642],[577,2905],{"className":2906,"style":2341},[646],[577,2908,765],{"className":2909},[651],[577,2911,2913],{"className":2912},[651],[577,2914,624],{"className":2915},[728],[577,2917,2919],{"className":2918},[651],"2769"," auf ",[577,2922,2924,2939],{"className":2923},[580],[577,2925,2927],{"className":2926},[584],[586,2928,2929],{"xmlns":588},[590,2930,2931,2936],{},[593,2932,2933],{},[763,2934,2935],{},"0,1245",[631,2937,2938],{"encoding":633},"0{,}1245",[577,2940,2942],{"className":2941,"ariaHidden":623},[638],[577,2943,2945,2948,2951,2957],{"className":2944},[642],[577,2946],{"className":2947,"style":2341},[646],[577,2949,765],{"className":2950},[651],[577,2952,2954],{"className":2953},[651],[577,2955,624],{"className":2956},[728],[577,2958,2960],{"className":2959},[651],"1245",", ungefähr proportional zu ",[577,2963,2965,2978],{"className":2964},[580],[577,2966,2968],{"className":2967},[584],[586,2969,2970],{"xmlns":588},[590,2971,2972,2976],{},[593,2973,2974],{},[599,2975,915],{},[631,2977,915],{"encoding":633},[577,2979,2981],{"className":2980,"ariaHidden":623},[638],[577,2982,2984,2987],{"className":2983},[642],[577,2985],{"className":2986,"style":927},[646],[577,2988,915],{"className":2989},[651,655],[564,2991,2992,740,3087,3152,3153,2291,3249,1705,3308,3502,3503,3673,3674,2291,3776,3837,3838,3918,3919,4026],{},[577,2993,2995,3022],{"className":2994},[580],[577,2996,2998],{"className":2997},[584],[586,2999,3000],{"xmlns":588},[590,3001,3002,3019],{},[593,3003,3004,3010,3012,3015,3017],{},[596,3005,3006,3008],{},[599,3007,601],{},[603,3009,607],{"mathvariant":605,"lspace":606,"rspace":606},[603,3011,610],{},[603,3013,3014],{},"−",[763,3016,1813],{},[599,3018,601],{},[631,3020,3021],{"encoding":633},"y' = -2y",[577,3023,3025,3072],{"className":3024,"ariaHidden":623},[638],[577,3026,3028,3031,3063,3066,3069],{"className":3027},[642],[577,3029],{"className":3030,"style":647},[646],[577,3032,3034,3037],{"className":3033},[651],[577,3035,601],{"className":3036,"style":656},[651,655],[577,3038,3040],{"className":3039},[660],[577,3041,3043],{"className":3042},[664],[577,3044,3046],{"className":3045},[668],[577,3047,3049],{"className":3048,"style":673},[672],[577,3050,3051,3054],{"style":676},[577,3052],{"className":3053,"style":681},[680],[577,3055,3057],{"className":3056},[685,686,687,688],[577,3058,3060],{"className":3059},[651,688],[577,3061,607],{"className":3062},[651,688],[577,3064],{"className":3065,"style":699},[698],[577,3067,610],{"className":3068},[703],[577,3070],{"className":3071,"style":699},[698],[577,3073,3075,3078,3081,3084],{"className":3074},[642],[577,3076],{"className":3077,"style":2341},[646],[577,3079,3014],{"className":3080},[651],[577,3082,1813],{"className":3083},[651],[577,3085,601],{"className":3086,"style":656},[651,655],[577,3088,3090,3113],{"className":3089},[580],[577,3091,3093],{"className":3092},[584],[586,3094,3095],{"xmlns":588},[590,3096,3097,3111],{},[593,3098,3099,3101,3103,3105,3107,3109],{},[599,3100,601],{},[603,3102,617],{"stretchy":616},[763,3104,765],{},[603,3106,629],{"stretchy":616},[603,3108,610],{},[763,3110,1100],{},[631,3112,2114],{"encoding":633},[577,3114,3116,3143],{"className":3115,"ariaHidden":623},[638],[577,3117,3119,3122,3125,3128,3131,3134,3137,3140],{"className":3118},[642],[577,3120],{"className":3121,"style":713},[646],[577,3123,601],{"className":3124,"style":656},[651,655],[577,3126,617],{"className":3127},[721],[577,3129,765],{"className":3130},[651],[577,3132,629],{"className":3133},[739],[577,3135],{"className":3136,"style":699},[698],[577,3138,610],{"className":3139},[703],[577,3141],{"className":3142,"style":699},[698],[577,3144,3146,3149],{"className":3145},[642],[577,3147],{"className":3148,"style":1701},[646],[577,3150,1100],{"className":3151},[651]," mit der Lösung ",[577,3154,3156,3184],{"className":3155},[580],[577,3157,3159],{"className":3158},[584],[586,3160,3161],{"xmlns":588},[590,3162,3163,3181],{},[593,3164,3165,3167,3169],{},[599,3166,601],{},[603,3168,610],{},[596,3170,3171,3173],{},[599,3172,2175],{},[593,3174,3175,3177,3179],{},[603,3176,3014],{},[763,3178,1813],{},[599,3180,620],{},[631,3182,3183],{"encoding":633},"y = e^{-2t}",[577,3185,3187,3205],{"className":3186,"ariaHidden":623},[638],[577,3188,3190,3193,3196,3199,3202],{"className":3189},[642],[577,3191],{"className":3192,"style":858},[646],[577,3194,601],{"className":3195,"style":656},[651,655],[577,3197],{"className":3198,"style":699},[698],[577,3200,610],{"className":3201},[703],[577,3203],{"className":3204,"style":699},[698],[577,3206,3208,3211],{"className":3207},[642],[577,3209],{"className":3210,"style":2836},[646],[577,3212,3214,3217],{"className":3213},[651],[577,3215,2175],{"className":3216},[651,655],[577,3218,3220],{"className":3219},[660],[577,3221,3223],{"className":3222},[664],[577,3224,3226],{"className":3225},[668],[577,3227,3229],{"className":3228,"style":2836},[672],[577,3230,3231,3234],{"style":676},[577,3232],{"className":3233,"style":681},[680],[577,3235,3237],{"className":3236},[685,686,687,688],[577,3238,3240,3243,3246],{"className":3239},[651,688],[577,3241,3014],{"className":3242},[651,688],[577,3244,1813],{"className":3245},[651,688],[577,3247,620],{"className":3248},[651,655,688],[577,3250,3252,3269],{"className":3251},[580],[577,3253,3255],{"className":3254},[584],[586,3256,3257],{"xmlns":588},[590,3258,3259,3267],{},[593,3260,3261,3263,3265],{},[599,3262,915],{},[603,3264,610],{},[763,3266,2661],{},[631,3268,2664],{"encoding":633},[577,3270,3272,3290],{"className":3271,"ariaHidden":623},[638],[577,3273,3275,3278,3281,3284,3287],{"className":3274},[642],[577,3276],{"className":3277,"style":927},[646],[577,3279,915],{"className":3280},[651,655],[577,3282],{"className":3283,"style":699},[698],[577,3285,610],{"className":3286},[703],[577,3288],{"className":3289,"style":699},[698],[577,3291,3293,3296,3299,3305],{"className":3292},[642],[577,3294],{"className":3295,"style":2341},[646],[577,3297,765],{"className":3298},[651],[577,3300,3302],{"className":3301},[651],[577,3303,624],{"className":3304},[728],[577,3306,1100],{"className":3307},[651],[577,3309,3311,3353],{"className":3310},[580],[577,3312,3314],{"className":3313},[584],[586,3315,3316],{"xmlns":588},[590,3317,3318,3350],{},[593,3319,3320,3326,3328,3330,3332,3334,3337,3339,3341,3343,3345,3347],{},[758,3321,3322,3324],{},[599,3323,601],{},[763,3325,1100],{},[603,3327,610],{},[763,3329,1100],{},[603,3331,1097],{},[763,3333,2661],{},[603,3335,3336],{},"⋅",[603,3338,617],{"stretchy":616},[603,3340,3014],{},[763,3342,1813],{},[603,3344,629],{"stretchy":616},[603,3346,610],{},[763,3348,3349],{},"0,8",[631,3351,3352],{"encoding":633},"y_1 = 1 + 0{,}1 \\cdot (-2) = 0{,}8",[577,3354,3356,3411,3429,3456,3483],{"className":3355,"ariaHidden":623},[638],[577,3357,3359,3362,3402,3405,3408],{"className":3358},[642],[577,3360],{"className":3361,"style":858},[646],[577,3363,3365,3368],{"className":3364},[651],[577,3366,601],{"className":3367,"style":656},[651,655],[577,3369,3371],{"className":3370},[660],[577,3372,3374,3394],{"className":3373},[664,806],[577,3375,3377,3391],{"className":3376},[668],[577,3378,3380],{"className":3379,"style":813},[672],[577,3381,3382,3385],{"style":879},[577,3383],{"className":3384,"style":681},[680],[577,3386,3388],{"className":3387},[685,686,687,688],[577,3389,1100],{"className":3390},[651,688],[577,3392,830],{"className":3393},[829],[577,3395,3397],{"className":3396},[668],[577,3398,3400],{"className":3399,"style":837},[672],[577,3401],{},[577,3403],{"className":3404,"style":699},[698],[577,3406,610],{"className":3407},[703],[577,3409],{"className":3410,"style":699},[698],[577,3412,3414,3417,3420,3423,3426],{"className":3413},[642],[577,3415],{"className":3416,"style":2269},[646],[577,3418,1100],{"className":3419},[651],[577,3421],{"className":3422,"style":1251},[698],[577,3424,1097],{"className":3425},[1149],[577,3427],{"className":3428,"style":1251},[698],[577,3430,3432,3435,3438,3444,3447,3450,3453],{"className":3431},[642],[577,3433],{"className":3434,"style":2341},[646],[577,3436,765],{"className":3437},[651],[577,3439,3441],{"className":3440},[651],[577,3442,624],{"className":3443},[728],[577,3445,1100],{"className":3446},[651],[577,3448],{"className":3449,"style":1251},[698],[577,3451,3336],{"className":3452},[1149],[577,3454],{"className":3455,"style":1251},[698],[577,3457,3459,3462,3465,3468,3471,3474,3477,3480],{"className":3458},[642],[577,3460],{"className":3461,"style":713},[646],[577,3463,617],{"className":3464},[721],[577,3466,3014],{"className":3467},[651],[577,3469,1813],{"className":3470},[651],[577,3472,629],{"className":3473},[739],[577,3475],{"className":3476,"style":699},[698],[577,3478,610],{"className":3479},[703],[577,3481],{"className":3482,"style":699},[698],[577,3484,3486,3489,3492,3498],{"className":3485},[642],[577,3487],{"className":3488,"style":2341},[646],[577,3490,765],{"className":3491},[651],[577,3493,3495],{"className":3494},[651],[577,3496,624],{"className":3497},[728],[577,3499,3501],{"className":3500},[651],"8"," und nach zehn Schritten ",[577,3504,3506,3537],{"className":3505},[580],[577,3507,3509],{"className":3508},[584],[586,3510,3511],{"xmlns":588},[590,3512,3513,3534],{},[593,3514,3515,3521,3523,3529,3531],{},[758,3516,3517,3519],{},[599,3518,601],{},[763,3520,2723],{},[603,3522,610],{},[596,3524,3525,3527],{},[763,3526,3349],{},[763,3528,2723],{},[603,3530,1198],{},[763,3532,3533],{},"0,1074",[631,3535,3536],{"encoding":633},"y_{10} = 0{,}8^{10} \\approx 0{,}1074",[577,3538,3540,3598,3654],{"className":3539,"ariaHidden":623},[638],[577,3541,3543,3546,3589,3592,3595],{"className":3542},[642],[577,3544],{"className":3545,"style":858},[646],[577,3547,3549,3552],{"className":3548},[651],[577,3550,601],{"className":3551,"style":656},[651,655],[577,3553,3555],{"className":3554},[660],[577,3556,3558,3581],{"className":3557},[664,806],[577,3559,3561,3578],{"className":3560},[668],[577,3562,3564],{"className":3563,"style":813},[672],[577,3565,3566,3569],{"style":879},[577,3567],{"className":3568,"style":681},[680],[577,3570,3572],{"className":3571},[685,686,687,688],[577,3573,3575],{"className":3574},[651,688],[577,3576,2723],{"className":3577},[651,688],[577,3579,830],{"className":3580},[829],[577,3582,3584],{"className":3583},[668],[577,3585,3587],{"className":3586,"style":837},[672],[577,3588],{},[577,3590],{"className":3591,"style":699},[698],[577,3593,610],{"className":3594},[703],[577,3596],{"className":3597,"style":699},[698],[577,3599,3601,3604,3607,3613,3645,3648,3651],{"className":3600},[642],[577,3602],{"className":3603,"style":2808},[646],[577,3605,765],{"className":3606},[651],[577,3608,3610],{"className":3609},[651],[577,3611,624],{"className":3612},[728],[577,3614,3616,3619],{"className":3615},[651],[577,3617,3501],{"className":3618},[651],[577,3620,3622],{"className":3621},[660],[577,3623,3625],{"className":3624},[664],[577,3626,3628],{"className":3627},[668],[577,3629,3631],{"className":3630,"style":2836},[672],[577,3632,3633,3636],{"style":676},[577,3634],{"className":3635,"style":681},[680],[577,3637,3639],{"className":3638},[685,686,687,688],[577,3640,3642],{"className":3641},[651,688],[577,3643,2723],{"className":3644},[651,688],[577,3646],{"className":3647,"style":699},[698],[577,3649,1198],{"className":3650},[703],[577,3652],{"className":3653,"style":699},[698],[577,3655,3657,3660,3663,3669],{"className":3656},[642],[577,3658],{"className":3659,"style":2341},[646],[577,3661,765],{"className":3662},[651],[577,3664,3666],{"className":3665},[651],[577,3667,624],{"className":3668},[728],[577,3670,3672],{"className":3671},[651],"1074","; exakt ist ",[577,3675,3677,3704],{"className":3676},[580],[577,3678,3680],{"className":3679},[584],[586,3681,3682],{"xmlns":588},[590,3683,3684,3701],{},[593,3685,3686,3696,3698],{},[596,3687,3688,3690],{},[599,3689,2175],{},[593,3691,3692,3694],{},[603,3693,3014],{},[763,3695,1813],{},[603,3697,1198],{},[763,3699,3700],{},"0,1353",[631,3702,3703],{"encoding":633},"e^{-2} \\approx 0{,}1353",[577,3705,3707,3757],{"className":3706,"ariaHidden":623},[638],[577,3708,3710,3713,3748,3751,3754],{"className":3709},[642],[577,3711],{"className":3712,"style":2836},[646],[577,3714,3716,3719],{"className":3715},[651],[577,3717,2175],{"className":3718},[651,655],[577,3720,3722],{"className":3721},[660],[577,3723,3725],{"className":3724},[664],[577,3726,3728],{"className":3727},[668],[577,3729,3731],{"className":3730,"style":2836},[672],[577,3732,3733,3736],{"style":676},[577,3734],{"className":3735,"style":681},[680],[577,3737,3739],{"className":3738},[685,686,687,688],[577,3740,3742,3745],{"className":3741},[651,688],[577,3743,3014],{"className":3744},[651,688],[577,3746,1813],{"className":3747},[651,688],[577,3749],{"className":3750,"style":699},[698],[577,3752,1198],{"className":3753},[703],[577,3755],{"className":3756,"style":699},[698],[577,3758,3760,3763,3766,3772],{"className":3759},[642],[577,3761],{"className":3762,"style":2341},[646],[577,3764,765],{"className":3765},[651],[577,3767,3769],{"className":3768},[651],[577,3770,624],{"className":3771},[728],[577,3773,3775],{"className":3774},[651],"1353",[577,3777,3779,3798],{"className":3778},[580],[577,3780,3782],{"className":3781},[584],[586,3783,3784],{"xmlns":588},[590,3785,3786,3795],{},[593,3787,3788,3790,3792],{},[599,3789,915],{},[603,3791,610],{},[763,3793,3794],{},"1,5",[631,3796,3797],{"encoding":633},"h = 1{,}5",[577,3799,3801,3819],{"className":3800,"ariaHidden":623},[638],[577,3802,3804,3807,3810,3813,3816],{"className":3803},[642],[577,3805],{"className":3806,"style":927},[646],[577,3808,915],{"className":3809},[651,655],[577,3811],{"className":3812,"style":699},[698],[577,3814,610],{"className":3815},[703],[577,3817],{"className":3818,"style":699},[698],[577,3820,3822,3825,3828,3834],{"className":3821},[642],[577,3823],{"className":3824,"style":2341},[646],[577,3826,1100],{"className":3827},[651],[577,3829,3831],{"className":3830},[651],[577,3832,624],{"className":3833},[728],[577,3835,2545],{"className":3836},[651]," dagegen ist ",[577,3839,3841,3867],{"className":3840},[580],[577,3842,3844],{"className":3843},[584],[586,3845,3846],{"xmlns":588},[590,3847,3848,3864],{},[593,3849,3850,3852,3854,3856,3858,3860,3862],{},[763,3851,1100],{},[603,3853,1097],{},[599,3855,915],{},[599,3857,1581],{},[603,3859,610],{},[603,3861,3014],{},[763,3863,1813],{},[631,3865,3866],{"encoding":633},"1 + h\\lambda = -2",[577,3868,3870,3888,3906],{"className":3869,"ariaHidden":623},[638],[577,3871,3873,3876,3879,3882,3885],{"className":3872},[642],[577,3874],{"className":3875,"style":2269},[646],[577,3877,1100],{"className":3878},[651],[577,3880],{"className":3881,"style":1251},[698],[577,3883,1097],{"className":3884},[1149],[577,3886],{"className":3887,"style":1251},[698],[577,3889,3891,3894,3897,3900,3903],{"className":3890},[642],[577,3892],{"className":3893,"style":927},[646],[577,3895,1769],{"className":3896},[651,655],[577,3898],{"className":3899,"style":699},[698],[577,3901,610],{"className":3902},[703],[577,3904],{"className":3905,"style":699},[698],[577,3907,3909,3912,3915],{"className":3908},[642],[577,3910],{"className":3911,"style":2269},[646],[577,3913,3014],{"className":3914},[651],[577,3916,1813],{"className":3917},[651],", und die Näherung springt ",[577,3920,3922,3962],{"className":3921},[580],[577,3923,3925],{"className":3924},[584],[586,3926,3927],{"xmlns":588},[590,3928,3929,3959],{},[593,3930,3931,3933,3935,3937,3939,3941,3943,3945,3947,3949,3951,3954,3956],{},[763,3932,1100],{},[603,3934,624],{"separator":623},[603,3936,3014],{},[763,3938,1813],{},[603,3940,624],{"separator":623},[763,3942,2432],{},[603,3944,624],{"separator":623},[603,3946,3014],{},[763,3948,3501],{},[603,3950,624],{"separator":623},[763,3952,3953],{},"16",[603,3955,624],{"separator":623},[603,3957,3958],{},"…",[631,3960,3961],{"encoding":633},"1, -2, 4, -8, 16, \\ldots",[577,3963,3965],{"className":3964,"ariaHidden":623},[638],[577,3966,3968,3971,3974,3977,3980,3983,3986,3989,3992,3995,3998,4001,4004,4007,4010,4013,4016,4019,4022],{"className":3967},[642],[577,3969],{"className":3970,"style":2341},[646],[577,3972,1100],{"className":3973},[651],[577,3975,624],{"className":3976},[728],[577,3978],{"className":3979,"style":732},[698],[577,3981,3014],{"className":3982},[651],[577,3984,1813],{"className":3985},[651],[577,3987,624],{"className":3988},[728],[577,3990],{"className":3991,"style":732},[698],[577,3993,2432],{"className":3994},[651],[577,3996,624],{"className":3997},[728],[577,3999],{"className":4000,"style":732},[698],[577,4002,3014],{"className":4003},[651],[577,4005,3501],{"className":4006},[651],[577,4008,624],{"className":4009},[728],[577,4011],{"className":4012,"style":732},[698],[577,4014,3953],{"className":4015},[651],[577,4017,624],{"className":4018},[728],[577,4020],{"className":4021,"style":732},[698],[577,4023,3958],{"className":4024},[4025],"minner",", obwohl die echte Lösung abklingt.",[564,4028,4029,740,4136,1650,4201,4262],{},[577,4030,4032,4058],{"className":4031},[580],[577,4033,4035],{"className":4034},[584],[586,4036,4037],{"xmlns":588},[590,4038,4039,4055],{},[593,4040,4041,4047,4049,4051,4053],{},[596,4042,4043,4045],{},[599,4044,601],{},[603,4046,607],{"mathvariant":605,"lspace":606,"rspace":606},[603,4048,610],{},[599,4050,620],{},[603,4052,1097],{},[599,4054,601],{},[631,4056,4057],{"encoding":633},"y' = t + y",[577,4059,4061,4108,4127],{"className":4060,"ariaHidden":623},[638],[577,4062,4064,4067,4099,4102,4105],{"className":4063},[642],[577,4065],{"className":4066,"style":647},[646],[577,4068,4070,4073],{"className":4069},[651],[577,4071,601],{"className":4072,"style":656},[651,655],[577,4074,4076],{"className":4075},[660],[577,4077,4079],{"className":4078},[664],[577,4080,4082],{"className":4081},[668],[577,4083,4085],{"className":4084,"style":673},[672],[577,4086,4087,4090],{"style":676},[577,4088],{"className":4089,"style":681},[680],[577,4091,4093],{"className":4092},[685,686,687,688],[577,4094,4096],{"className":4095},[651,688],[577,4097,607],{"className":4098},[651,688],[577,4100],{"className":4101,"style":699},[698],[577,4103,610],{"className":4104},[703],[577,4106],{"className":4107,"style":699},[698],[577,4109,4111,4115,4118,4121,4124],{"className":4110},[642],[577,4112],{"className":4113,"style":4114},[646],"height:0.6984em;vertical-align:-0.0833em;",[577,4116,620],{"className":4117},[651,655],[577,4119],{"className":4120,"style":1251},[698],[577,4122,1097],{"className":4123},[1149],[577,4125],{"className":4126,"style":1251},[698],[577,4128,4130,4133],{"className":4129},[642],[577,4131],{"className":4132,"style":858},[646],[577,4134,601],{"className":4135,"style":656},[651,655],[577,4137,4139,4162],{"className":4138},[580],[577,4140,4142],{"className":4141},[584],[586,4143,4144],{"xmlns":588},[590,4145,4146,4160],{},[593,4147,4148,4150,4152,4154,4156,4158],{},[599,4149,601],{},[603,4151,617],{"stretchy":616},[763,4153,765],{},[603,4155,629],{"stretchy":616},[603,4157,610],{},[763,4159,1100],{},[631,4161,2114],{"encoding":633},[577,4163,4165,4192],{"className":4164,"ariaHidden":623},[638],[577,4166,4168,4171,4174,4177,4180,4183,4186,4189],{"className":4167},[642],[577,4169],{"className":4170,"style":713},[646],[577,4172,601],{"className":4173,"style":656},[651,655],[577,4175,617],{"className":4176},[721],[577,4178,765],{"className":4179},[651],[577,4181,629],{"className":4182},[739],[577,4184],{"className":4185,"style":699},[698],[577,4187,610],{"className":4188},[703],[577,4190],{"className":4191,"style":699},[698],[577,4193,4195,4198],{"className":4194},[642],[577,4196],{"className":4197,"style":1701},[646],[577,4199,1100],{"className":4200},[651],[577,4202,4204,4223],{"className":4203},[580],[577,4205,4207],{"className":4206},[584],[586,4208,4209],{"xmlns":588},[590,4210,4211,4220],{},[593,4212,4213,4215,4217],{},[599,4214,915],{},[603,4216,610],{},[763,4218,4219],{},"0,5",[631,4221,4222],{"encoding":633},"h = 0{,}5",[577,4224,4226,4244],{"className":4225,"ariaHidden":623},[638],[577,4227,4229,4232,4235,4238,4241],{"className":4228},[642],[577,4230],{"className":4231,"style":927},[646],[577,4233,915],{"className":4234},[651,655],[577,4236],{"className":4237,"style":699},[698],[577,4239,610],{"className":4240},[703],[577,4242],{"className":4243,"style":699},[698],[577,4245,4247,4250,4253,4259],{"className":4246},[642],[577,4248],{"className":4249,"style":2341},[646],[577,4251,765],{"className":4252},[651],[577,4254,4256],{"className":4255},[651],[577,4257,624],{"className":4258},[728],[577,4260,2545],{"className":4261},[651],":",[577,4264,4266],{"className":4265},[2412],[577,4267,4269,4346],{"className":4268},[580],[577,4270,4272],{"className":4271},[584],[586,4273,4274],{"xmlns":588,"display":2421},[590,4275,4276,4343],{},[593,4277,4278,4284,4286,4288,4290,4292,4294,4296,4298,4300,4302,4304,4306,4308,4310,4312,4318,4320,4322,4324,4326,4328,4330,4332,4334,4336,4338,4340],{},[758,4279,4280,4282],{},[599,4281,601],{},[763,4283,1100],{},[603,4285,610],{},[763,4287,1100],{},[603,4289,1097],{},[763,4291,4219],{},[603,4293,3336],{},[603,4295,617],{"stretchy":616},[763,4297,765],{},[603,4299,1097],{},[763,4301,1100],{},[603,4303,629],{"stretchy":616},[603,4305,610],{},[763,4307,3794],{},[603,4309,624],{"separator":623},[698,4311],{"width":2451},[758,4313,4314,4316],{},[599,4315,601],{},[763,4317,1813],{},[603,4319,610],{},[763,4321,3794],{},[603,4323,1097],{},[763,4325,4219],{},[603,4327,3336],{},[603,4329,617],{"stretchy":616},[763,4331,4219],{},[603,4333,1097],{},[763,4335,3794],{},[603,4337,629],{"stretchy":616},[603,4339,610],{},[763,4341,4342],{},"2,5",[631,4344,4345],{"encoding":633},"y_1 = 1 + 0{,}5 \\cdot (0 + 1) = 1{,}5, \\qquad y_2 = 1{,}5 + 0{,}5 \\cdot (0{,}5 + 1{,}5) = 2{,}5",[577,4347,4349,4404,4422,4449,4470,4491,4567,4594,4621,4651,4681],{"className":4348,"ariaHidden":623},[638],[577,4350,4352,4355,4395,4398,4401],{"className":4351},[642],[577,4353],{"className":4354,"style":858},[646],[577,4356,4358,4361],{"className":4357},[651],[577,4359,601],{"className":4360,"style":656},[651,655],[577,4362,4364],{"className":4363},[660],[577,4365,4367,4387],{"className":4366},[664,806],[577,4368,4370,4384],{"className":4369},[668],[577,4371,4373],{"className":4372,"style":813},[672],[577,4374,4375,4378],{"style":879},[577,4376],{"className":4377,"style":681},[680],[577,4379,4381],{"className":4380},[685,686,687,688],[577,4382,1100],{"className":4383},[651,688],[577,4385,830],{"className":4386},[829],[577,4388,4390],{"className":4389},[668],[577,4391,4393],{"className":4392,"style":837},[672],[577,4394],{},[577,4396],{"className":4397,"style":699},[698],[577,4399,610],{"className":4400},[703],[577,4402],{"className":4403,"style":699},[698],[577,4405,4407,4410,4413,4416,4419],{"className":4406},[642],[577,4408],{"className":4409,"style":2269},[646],[577,4411,1100],{"className":4412},[651],[577,4414],{"className":4415,"style":1251},[698],[577,4417,1097],{"className":4418},[1149],[577,4420],{"className":4421,"style":1251},[698],[577,4423,4425,4428,4431,4437,4440,4443,4446],{"className":4424},[642],[577,4426],{"className":4427,"style":2341},[646],[577,4429,765],{"className":4430},[651],[577,4432,4434],{"className":4433},[651],[577,4435,624],{"className":4436},[728],[577,4438,2545],{"className":4439},[651],[577,4441],{"className":4442,"style":1251},[698],[577,4444,3336],{"className":4445},[1149],[577,4447],{"className":4448,"style":1251},[698],[577,4450,4452,4455,4458,4461,4464,4467],{"className":4451},[642],[577,4453],{"className":4454,"style":713},[646],[577,4456,617],{"className":4457},[721],[577,4459,765],{"className":4460},[651],[577,4462],{"className":4463,"style":1251},[698],[577,4465,1097],{"className":4466},[1149],[577,4468],{"className":4469,"style":1251},[698],[577,4471,4473,4476,4479,4482,4485,4488],{"className":4472},[642],[577,4474],{"className":4475,"style":713},[646],[577,4477,1100],{"className":4478},[651],[577,4480,629],{"className":4481},[739],[577,4483],{"className":4484,"style":699},[698],[577,4486,610],{"className":4487},[703],[577,4489],{"className":4490,"style":699},[698],[577,4492,4494,4497,4500,4506,4509,4512,4515,4518,4558,4561,4564],{"className":4493},[642],[577,4495],{"className":4496,"style":2341},[646],[577,4498,1100],{"className":4499},[651],[577,4501,4503],{"className":4502},[651],[577,4504,624],{"className":4505},[728],[577,4507,2545],{"className":4508},[651],[577,4510,624],{"className":4511},[728],[577,4513],{"className":4514,"style":2605},[698],[577,4516],{"className":4517,"style":732},[698],[577,4519,4521,4524],{"className":4520},[651],[577,4522,601],{"className":4523,"style":656},[651,655],[577,4525,4527],{"className":4526},[660],[577,4528,4530,4550],{"className":4529},[664,806],[577,4531,4533,4547],{"className":4532},[668],[577,4534,4536],{"className":4535,"style":813},[672],[577,4537,4538,4541],{"style":879},[577,4539],{"className":4540,"style":681},[680],[577,4542,4544],{"className":4543},[685,686,687,688],[577,4545,1813],{"className":4546},[651,688],[577,4548,830],{"className":4549},[829],[577,4551,4553],{"className":4552},[668],[577,4554,4556],{"className":4555,"style":837},[672],[577,4557],{},[577,4559],{"className":4560,"style":699},[698],[577,4562,610],{"className":4563},[703],[577,4565],{"className":4566,"style":699},[698],[577,4568,4570,4573,4576,4582,4585,4588,4591],{"className":4569},[642],[577,4571],{"className":4572,"style":2341},[646],[577,4574,1100],{"className":4575},[651],[577,4577,4579],{"className":4578},[651],[577,4580,624],{"className":4581},[728],[577,4583,2545],{"className":4584},[651],[577,4586],{"className":4587,"style":1251},[698],[577,4589,1097],{"className":4590},[1149],[577,4592],{"className":4593,"style":1251},[698],[577,4595,4597,4600,4603,4609,4612,4615,4618],{"className":4596},[642],[577,4598],{"className":4599,"style":2341},[646],[577,4601,765],{"className":4602},[651],[577,4604,4606],{"className":4605},[651],[577,4607,624],{"className":4608},[728],[577,4610,2545],{"className":4611},[651],[577,4613],{"className":4614,"style":1251},[698],[577,4616,3336],{"className":4617},[1149],[577,4619],{"className":4620,"style":1251},[698],[577,4622,4624,4627,4630,4633,4639,4642,4645,4648],{"className":4623},[642],[577,4625],{"className":4626,"style":713},[646],[577,4628,617],{"className":4629},[721],[577,4631,765],{"className":4632},[651],[577,4634,4636],{"className":4635},[651],[577,4637,624],{"className":4638},[728],[577,4640,2545],{"className":4641},[651],[577,4643],{"className":4644,"style":1251},[698],[577,4646,1097],{"className":4647},[1149],[577,4649],{"className":4650,"style":1251},[698],[577,4652,4654,4657,4660,4666,4669,4672,4675,4678],{"className":4653},[642],[577,4655],{"className":4656,"style":713},[646],[577,4658,1100],{"className":4659},[651],[577,4661,4663],{"className":4662},[651],[577,4664,624],{"className":4665},[728],[577,4667,2545],{"className":4668},[651],[577,4670,629],{"className":4671},[739],[577,4673],{"className":4674,"style":699},[698],[577,4676,610],{"className":4677},[703],[577,4679],{"className":4680,"style":699},[698],[577,4682,4684,4687,4690,4696],{"className":4683},[642],[577,4685],{"className":4686,"style":2341},[646],[577,4688,1813],{"className":4689},[651],[577,4691,4693],{"className":4692},[651],[577,4694,624],{"className":4695},[728],[577,4697,2545],{"className":4698},[651],[564,4700,4701,4702,4833,4834,1168],{},"Die exakte Lösung ist ",[577,4703,4705,4737],{"className":4704},[580],[577,4706,4708],{"className":4707},[584],[586,4709,4710],{"xmlns":588},[590,4711,4712,4734],{},[593,4713,4714,4716,4718,4720,4726,4728,4730,4732],{},[599,4715,601],{},[603,4717,610],{},[763,4719,1813],{},[596,4721,4722,4724],{},[599,4723,2175],{},[599,4725,620],{},[603,4727,3014],{},[599,4729,620],{},[603,4731,3014],{},[763,4733,1100],{},[631,4735,4736],{"encoding":633},"y = 2e^t - t - 1",[577,4738,4740,4758,4806,4824],{"className":4739,"ariaHidden":623},[638],[577,4741,4743,4746,4749,4752,4755],{"className":4742},[642],[577,4744],{"className":4745,"style":858},[646],[577,4747,601],{"className":4748,"style":656},[651,655],[577,4750],{"className":4751,"style":699},[698],[577,4753,610],{"className":4754},[703],[577,4756],{"className":4757,"style":699},[698],[577,4759,4761,4765,4768,4797,4800,4803],{"className":4760},[642],[577,4762],{"className":4763,"style":4764},[646],"height:0.8769em;vertical-align:-0.0833em;",[577,4766,1813],{"className":4767},[651],[577,4769,4771,4774],{"className":4770},[651],[577,4772,2175],{"className":4773},[651,655],[577,4775,4777],{"className":4776},[660],[577,4778,4780],{"className":4779},[664],[577,4781,4783],{"className":4782},[668],[577,4784,4786],{"className":4785,"style":2208},[672],[577,4787,4788,4791],{"style":676},[577,4789],{"className":4790,"style":681},[680],[577,4792,4794],{"className":4793},[685,686,687,688],[577,4795,620],{"className":4796},[651,655,688],[577,4798],{"className":4799,"style":1251},[698],[577,4801,3014],{"className":4802},[1149],[577,4804],{"className":4805,"style":1251},[698],[577,4807,4809,4812,4815,4818,4821],{"className":4808},[642],[577,4810],{"className":4811,"style":4114},[646],[577,4813,620],{"className":4814},[651,655],[577,4816],{"className":4817,"style":1251},[698],[577,4819,3014],{"className":4820},[1149],[577,4822],{"className":4823,"style":1251},[698],[577,4825,4827,4830],{"className":4826},[642],[577,4828],{"className":4829,"style":1701},[646],[577,4831,1100],{"className":4832},[651],", also ",[577,4835,4837,4872],{"className":4836},[580],[577,4838,4840],{"className":4839},[584],[586,4841,4842],{"xmlns":588},[590,4843,4844,4869],{},[593,4845,4846,4848,4850,4852,4854,4856,4858,4860,4862,4864,4866],{},[599,4847,601],{},[603,4849,617],{"stretchy":616},[763,4851,1100],{},[603,4853,629],{"stretchy":616},[603,4855,610],{},[763,4857,1813],{},[599,4859,2175],{},[603,4861,3014],{},[763,4863,1813],{},[603,4865,1198],{},[763,4867,4868],{},"3,4366",[631,4870,4871],{"encoding":633},"y(1) = 2e - 2 \\approx 3{,}4366",[577,4873,4875,4902,4923,4941],{"className":4874,"ariaHidden":623},[638],[577,4876,4878,4881,4884,4887,4890,4893,4896,4899],{"className":4877},[642],[577,4879],{"className":4880,"style":713},[646],[577,4882,601],{"className":4883,"style":656},[651,655],[577,4885,617],{"className":4886},[721],[577,4888,1100],{"className":4889},[651],[577,4891,629],{"className":4892},[739],[577,4894],{"className":4895,"style":699},[698],[577,4897,610],{"className":4898},[703],[577,4900],{"className":4901,"style":699},[698],[577,4903,4905,4908,4911,4914,4917,4920],{"className":4904},[642],[577,4906],{"className":4907,"style":2269},[646],[577,4909,1813],{"className":4910},[651],[577,4912,2175],{"className":4913},[651,655],[577,4915],{"className":4916,"style":1251},[698],[577,4918,3014],{"className":4919},[1149],[577,4921],{"className":4922,"style":1251},[698],[577,4924,4926,4929,4932,4935,4938],{"className":4925},[642],[577,4927],{"className":4928,"style":1701},[646],[577,4930,1813],{"className":4931},[651],[577,4933],{"className":4934,"style":699},[698],[577,4936,1198],{"className":4937},[703],[577,4939],{"className":4940,"style":699},[698],[577,4942,4944,4947,4951,4957],{"className":4943},[642],[577,4945],{"className":4946,"style":2341},[646],[577,4948,4950],{"className":4949},[651],"3",[577,4952,4954],{"className":4953},[651],[577,4955,624],{"className":4956},[728],[577,4958,4960],{"className":4959},[651],"4366",[559,4962,4964],{"id":4963},"typische-fehler","Typische Fehler",[1364,4966,4967,4970,5174,5177],{},[1367,4968,4969],{},"Die Steigung am neuen statt am alten Punkt auswerten. Das wäre das implizite Euler-Verfahren.",[1367,4971,4972,4973,5030,5031,5102,5103,5173],{},"Bei ",[577,4974,4976,5000],{"className":4975},[580],[577,4977,4979],{"className":4978},[584],[586,4980,4981],{"xmlns":588},[590,4982,4983,4997],{},[593,4984,4985,4987,4989,4991,4993,4995],{},[599,4986,613],{},[603,4988,617],{"stretchy":616},[599,4990,620],{},[603,4992,624],{"separator":623},[599,4994,601],{},[603,4996,629],{"stretchy":616},[631,4998,4999],{"encoding":633},"f(t, y)",[577,5001,5003],{"className":5002,"ariaHidden":623},[638],[577,5004,5006,5009,5012,5015,5018,5021,5024,5027],{"className":5005},[642],[577,5007],{"className":5008,"style":713},[646],[577,5010,613],{"className":5011,"style":717},[651,655],[577,5013,617],{"className":5014},[721],[577,5016,620],{"className":5017},[651,655],[577,5019,624],{"className":5020},[728],[577,5022],{"className":5023,"style":732},[698],[577,5025,601],{"className":5026,"style":656},[651,655],[577,5028,629],{"className":5029},[739]," die Zeit ",[577,5032,5034,5052],{"className":5033},[580],[577,5035,5037],{"className":5036},[584],[586,5038,5039],{"xmlns":588},[590,5040,5041,5049],{},[593,5042,5043],{},[758,5044,5045,5047],{},[599,5046,620],{},[599,5048,954],{},[631,5050,5051],{"encoding":633},"t_k",[577,5053,5055],{"className":5054,"ariaHidden":623},[638],[577,5056,5058,5062],{"className":5057},[642],[577,5059],{"className":5060,"style":5061},[646],"height:0.7651em;vertical-align:-0.15em;",[577,5063,5065,5068],{"className":5064},[651],[577,5066,620],{"className":5067},[651,655],[577,5069,5071],{"className":5070},[660],[577,5072,5074,5094],{"className":5073},[664,806],[577,5075,5077,5091],{"className":5076},[668],[577,5078,5080],{"className":5079,"style":1001},[672],[577,5081,5082,5085],{"style":816},[577,5083],{"className":5084,"style":681},[680],[577,5086,5088],{"className":5087},[685,686,687,688],[577,5089,954],{"className":5090,"style":1013},[651,655,688],[577,5092,830],{"className":5093},[829],[577,5095,5097],{"className":5096},[668],[577,5098,5100],{"className":5099,"style":837},[672],[577,5101],{}," nicht mitführen und z.B. immer ",[577,5104,5106,5124],{"className":5105},[580],[577,5107,5109],{"className":5108},[584],[586,5110,5111],{"xmlns":588},[590,5112,5113,5121],{},[593,5114,5115],{},[758,5116,5117,5119],{},[599,5118,620],{},[763,5120,765],{},[631,5122,5123],{"encoding":633},"t_0",[577,5125,5127],{"className":5126,"ariaHidden":623},[638],[577,5128,5130,5133],{"className":5129},[642],[577,5131],{"className":5132,"style":5061},[646],[577,5134,5136,5139],{"className":5135},[651],[577,5137,620],{"className":5138},[651,655],[577,5140,5142],{"className":5141},[660],[577,5143,5145,5165],{"className":5144},[664,806],[577,5146,5148,5162],{"className":5147},[668],[577,5149,5151],{"className":5150,"style":813},[672],[577,5152,5153,5156],{"style":816},[577,5154],{"className":5155,"style":681},[680],[577,5157,5159],{"className":5158},[685,686,687,688],[577,5160,765],{"className":5161},[651,688],[577,5163,830],{"className":5164},[829],[577,5166,5168],{"className":5167},[668],[577,5169,5171],{"className":5170,"style":837},[672],[577,5172],{}," einsetzen.",[1367,5175,5176],{},"Eine zu große Schrittweite wählen. Neben großem Fehler droht bei abklingenden Lösungen Instabilität.",[1367,5178,5179,5180,5249,5250,5281,5282,5443],{},"Die Anzahl der Schritte falsch bestimmen: Von ",[577,5181,5183,5200],{"className":5182},[580],[577,5184,5186],{"className":5185},[584],[586,5187,5188],{"xmlns":588},[590,5189,5190,5198],{},[593,5191,5192],{},[758,5193,5194,5196],{},[599,5195,620],{},[763,5197,765],{},[631,5199,5123],{"encoding":633},[577,5201,5203],{"className":5202,"ariaHidden":623},[638],[577,5204,5206,5209],{"className":5205},[642],[577,5207],{"className":5208,"style":5061},[646],[577,5210,5212,5215],{"className":5211},[651],[577,5213,620],{"className":5214},[651,655],[577,5216,5218],{"className":5217},[660],[577,5219,5221,5241],{"className":5220},[664,806],[577,5222,5224,5238],{"className":5223},[668],[577,5225,5227],{"className":5226,"style":813},[672],[577,5228,5229,5232],{"style":816},[577,5230],{"className":5231,"style":681},[680],[577,5233,5235],{"className":5234},[685,686,687,688],[577,5236,765],{"className":5237},[651,688],[577,5239,830],{"className":5240},[829],[577,5242,5244],{"className":5243},[668],[577,5245,5247],{"className":5246,"style":837},[672],[577,5248],{}," bis ",[577,5251,5253,5267],{"className":5252},[580],[577,5254,5256],{"className":5255},[584],[586,5257,5258],{"xmlns":588},[590,5259,5260,5265],{},[593,5261,5262],{},[599,5263,5264],{},"T",[631,5266,5264],{"encoding":633},[577,5268,5270],{"className":5269,"ariaHidden":623},[638],[577,5271,5273,5277],{"className":5272},[642],[577,5274],{"className":5275,"style":5276},[646],"height:0.6833em;",[577,5278,5264],{"className":5279,"style":5280},[651,655],"margin-right:0.1389em;"," sind es ",[577,5283,5285,5313],{"className":5284},[580],[577,5286,5288],{"className":5287},[584],[586,5289,5290],{"xmlns":588},[590,5291,5292,5310],{},[593,5293,5294],{},[1809,5295,5296,5308],{},[593,5297,5298,5300,5302],{},[599,5299,5264],{},[603,5301,3014],{},[758,5303,5304,5306],{},[599,5305,620],{},[763,5307,765],{},[599,5309,915],{},[631,5311,5312],{"encoding":633},"\\frac{T - t_0}{h}",[577,5314,5316],{"className":5315,"ariaHidden":623},[638],[577,5317,5319,5323],{"className":5318},[642],[577,5320],{"className":5321,"style":5322},[646],"height:1.2334em;vertical-align:-0.345em;",[577,5324,5326,5329,5440],{"className":5325},[651],[577,5327],{"className":5328},[721,1859],[577,5330,5332],{"className":5331},[1809],[577,5333,5335,5431],{"className":5334},[664,806],[577,5336,5338,5428],{"className":5337},[668],[577,5339,5342,5356,5364],{"className":5340,"style":5341},[672],"height:0.8884em;",[577,5343,5344,5347],{"style":1875},[577,5345],{"className":5346,"style":1879},[680],[577,5348,5350],{"className":5349},[685,686,687,688],[577,5351,5353],{"className":5352},[651,688],[577,5354,915],{"className":5355},[651,655,688],[577,5357,5358,5361],{"style":1897},[577,5359],{"className":5360,"style":1879},[680],[577,5362],{"className":5363,"style":1905},[1904],[577,5365,5367,5370],{"style":5366},"top:-3.4101em;",[577,5368],{"className":5369,"style":1879},[680],[577,5371,5373],{"className":5372},[685,686,687,688],[577,5374,5376,5379,5382],{"className":5375},[651,688],[577,5377,5264],{"className":5378,"style":5280},[651,655,688],[577,5380,3014],{"className":5381},[1149,688],[577,5383,5385,5388],{"className":5384},[651,688],[577,5386,620],{"className":5387},[651,655,688],[577,5389,5391],{"className":5390},[660],[577,5392,5394,5419],{"className":5393},[664,806],[577,5395,5397,5416],{"className":5396},[668],[577,5398,5401],{"className":5399,"style":5400},[672],"height:0.3173em;",[577,5402,5404,5408],{"style":5403},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[577,5405],{"className":5406,"style":5407},[680],"height:2.5em;",[577,5409,5413],{"className":5410},[685,5411,5412,688],"reset-size3","size1",[577,5414,765],{"className":5415},[651,688],[577,5417,830],{"className":5418},[829],[577,5420,5422],{"className":5421},[668],[577,5423,5426],{"className":5424,"style":5425},[672],"height:0.143em;",[577,5427],{},[577,5429,830],{"className":5430},[829],[577,5432,5434],{"className":5433},[668],[577,5435,5438],{"className":5436,"style":5437},[672],"height:0.345em;",[577,5439],{},[577,5441],{"className":5442},[739,1859]," Schritte.",{"title":5445,"searchDepth":5446,"depth":5446,"links":5447},"",2,[5448,5449,5450],{"id":561,"depth":5446,"text":562},{"id":2000,"depth":5446,"text":2001},{"id":4963,"depth":5446,"text":4964},[5452,5455,5458,5461,5464,5467,5470,5473,5476,5479,5482,5485,5487,5490,5493,5496],{"lhs":5453,"rhs":5454},"y + h*y","y*(1 + h)",{"lhs":5456,"rhs":5457},"1.25^4","2.44140625",{"lhs":5459,"rhs":5460},"round(1.25^4, 4)","2.4414",{"lhs":5462,"rhs":5463},"round(1.1^10, 4)","2.5937",{"lhs":5465,"rhs":5466},"round(exp(1), 4)","2.7183",{"lhs":5468,"rhs":5469},"round(exp(1) - 1.25^4, 4)","0.2769",{"lhs":5471,"rhs":5472},"round(exp(1) - 1.1^10, 4)","0.1245",{"lhs":5474,"rhs":5475},"1 + 0.1*(-2*1)","0.8",{"lhs":5477,"rhs":5478},"round(0.8^10, 4)","0.1074",{"lhs":5480,"rhs":5481},"round(exp(-2), 4)","0.1353",{"lhs":5483,"rhs":5484},"1 - 1.5*2","-2",{"lhs":5486,"rhs":3953},"(1 - 1.5*2)^4",{"lhs":5488,"rhs":5489},"1 + 0.5*(0 + 1)","1.5",{"lhs":5491,"rhs":5492},"1.5 + 0.5*(0.5 + 1.5)","2.5",{"lhs":5494,"rhs":5495},"2*exp(1) - 1 - 1","2*exp(1) - 2",{"lhs":5497,"rhs":5498},"round(2*exp(1) - 2, 4)","3.4366","y'(t) = f(t, y(t)),\\ y(t_0) = y_0,\\ h > 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>y\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y'(t) = f(t, y(t)),\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0019em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mclose\">))\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>t\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y(t_0) = y_0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","euler-method","y_{k+1} = y_k + h \\cdot f(t_k, y_k), \\qquad t_{k+1} = t_k + h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>t\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmi>t\u003C\u002Fmi>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>t\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y_{k+1} = y_k + h \\cdot f(t_k, y_k), \\qquad t_{k+1} = t_k + h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.2083em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y_k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan 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